EdnddlmZddlmZddlmZddlmZddlm Z m Z m Z GddeZ Gd d eZ d S) )S)_sympify)KroneckerDelta) MatrixExpr) ZeroMatrixIdentity OneMatrixczeZdZdZfdZedZedZdZdZ dZ dZ e xZ Z d Zd ZxZS) PermutationMatrixaA Permutation Matrix Parameters ========== perm : Permutation The permutation the matrix uses. The size of the permutation determines the matrix size. See the documentation of :class:`sympy.combinatorics.permutations.Permutation` for the further information of how to create a permutation object. Examples ======== >>> from sympy import Matrix, PermutationMatrix >>> from sympy.combinatorics import Permutation Creating a permutation matrix: >>> p = Permutation(1, 2, 0) >>> P = PermutationMatrix(p) >>> P = P.as_explicit() >>> P Matrix([ [0, 1, 0], [0, 0, 1], [1, 0, 0]]) Permuting a matrix row and column: >>> M = Matrix([0, 1, 2]) >>> Matrix(P*M) Matrix([ [1], [2], [0]]) >>> Matrix(M.T*P) Matrix([[2, 0, 1]]) See Also ======== sympy.combinatorics.permutations.Permutation cddlm}t|}t||s"t d|t ||S)Nr Permutationz({} must be a SymPy Permutation instance.) sympy.combinatorics.permutationsrr isinstance ValueErrorformatsuper__new__)clspermr __class__s Flib/python3.11/site-packages/sympy/matrices/expressions/permutation.pyrzPermutationMatrix.__new__;ss@@@@@@~~$ ,, I:AA$GGII IwwsD)))c.|jdj}||fSNr)argssize)selfrs rshapezPermutationMatrix.shapeEsy| d|rc&|jdjSr)r is_Identityrs rr"zPermutationMatrix.is_IdentityJsy|''rc <|jrt|jS|S)N)r"r rows)rhintss rdoitzPermutationMatrix.doitNs"   'DI&& & rc b|jd}t|||Sr)rrapply)rijkwargsrs r_entryzPermutationMatrix._entrySs'y|djjmmQ///rc`t|jd|zSr)r rr')rexps r _eval_powerzPermutationMatrix._eval_powerWs' 1!455::<<).0r*ps r zFPermutationMatrix._eval_rewrite_as_BlockDiagMatrix..s222qQU222r) rr blockmatrixr<rfull_cyclic_formlenmaxappendr )rrr,rr<rrC cycles_picksabcflagcyclelmtemppick new_cycles new_cyclematr@s @r _eval_rewrite_as_BlockDiagMatrixz2PermutationMatrix._eval_rewrite_as_BlockDiagMatrixgsp@@@@@@000000y|0 1a%! ! EE AE A q51q5=D!7DAAA ''000FAAq51uA ) E***$++D111$aC E***Q1uA ) E***$++D111$aC E***Q   DJA  2222E222 !!),,,SZZ FA;z**D#D))C KK    %%r)__name__ __module__ __qualname____doc__rpropertyr r"r'r-r0r3_eval_transpose _eval_adjointr:rT __classcell__rs@rr r s//b*****X((X( 000===555'43Om""">&>&>&>&>&>&>&rr cZeZdZdZejffd ZddZedZ dZ dZ xZ S) MatrixPermuteavSymbolic representation for permuting matrix rows or columns. Parameters ========== perm : Permutation, PermutationMatrix The permutation to use for permuting the matrix. The permutation can be resized to the suitable one, axis : 0 or 1 The axis to permute alongside. If `0`, it will permute the matrix rows. If `1`, it will permute the matrix columns. Notes ===== This follows the same notation used in :meth:`sympy.matrices.common.MatrixCommon.permute`. Examples ======== >>> from sympy import Matrix, MatrixPermute >>> from sympy.combinatorics import Permutation Permuting the matrix rows: >>> p = Permutation(1, 2, 0) >>> A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) >>> B = MatrixPermute(A, p, axis=0) >>> B.as_explicit() Matrix([ [4, 5, 6], [7, 8, 9], [1, 2, 3]]) Permuting the matrix columns: >>> B = MatrixPermute(A, p, axis=1) >>> B.as_explicit() Matrix([ [2, 3, 1], [5, 6, 4], [8, 9, 7]]) See Also ======== sympy.matrices.common.MatrixCommon.permute cddlm}t|}|js"t d|t|}t |tr |jd}t ||s"t d|t|}|dvrt d|j |}||j krI | |}n2#t$r%t d|||wxYwt ||||S)Nrrz#{} must be a SymPy matrix instance.z>{} must be a SymPy Permutation or a PermutationMatrix instance)rrzThe axis must be 0 or 1.zsSize does not match between the permutation {} and the matrix {} threaded over the axis {} and cannot be converted.)rrr is_Matrixrrrr rr rresizerr)rrSraxisrmat_sizers rrzMatrixPermute.__new__sn@@@@@@smm} D5<) rr'r"rZeror r6rrr r_)rrfr&rSrrcs rr'zMatrixPermute.doits)T4  1#(.....C4900$0%00D   J ? 3qv~ 3(... 3(r222 cJ 2 3 3 J c= ) ) HchqkT.A H !dSXa[.@$GG G rc&|jdjSr)rr r#s rr zMatrixPermute.shapesy|!!rc |j\}}}|dkr||||fS|dkr||||fSdS)Nrr)rr))rr*r+r,rSrrcs rr-zMatrixPermute._entryse)T4 19 )tzz!}}a'( ( QY )q$**Q--'( ( ) )rcddlm}|j\}}}|dd}|r||}|dkr|t ||S|dkr||t |dzSdS)Nr)MatMulrfTrr2)matmulrlrgetrewriter )rrr,rlrSrrcrfs r_eval_rewrite_as_MatMulz%MatrixPermute._eval_rewrite_as_MatMul"s"""""")T4zz&$''  &++f%%C 19 <6+D11377 7 QY <6#0r::;; ; < rrrvs''''''******4444444444\&\&\&\&\& \&\&\&~G<G<G<G<G